Chris Wood bridged a 44-year gap and also helped the Clarets create some modern-day history as they guaranteed a top-10 finish in the Premier League.
Wood claimed his 13th league goal of the season to become the highest Burnley scorer in a top-flight campaign since Peter Noble and Ray Hankin posted that total in 1975/76.
The New Zealander’s fine finish in first-half stoppage time also set up a 15th Premier League win of the season – confirmed by Ben Godrey’s late own-goal – to set a new high for the Clarets.
And with the nine-man Canaries, who had two men sent off before half-time, unable to offer any sort of response on their way back towards the Championship, Sean Dyche’s men were also able to match the 54-point record Premier League tally they chalked up when finishing seventh two seasons ago.
That was enough to earn a place in the Europa League – something that remains mathematically possible again this time around.
But the Clarets will need their rivals to drop points in mid-week before finishing the season at home to Brighton next Sunday when they will look to extend a remarkable unbeaten run to eight games.
Charlie Taylor’s injury-enforced absence had meant one change for the Clarets and a first league start since early October for Johann Berg Gudmundsson, as well as a slot on the Clarets’ bench for the first time for U23s’ striker Joel Mumbongo.
Norwich also made one change from mid-week with Emiliano Buendia returning – a comeback that lasted only 35 minutes before he was shown the red card by referee Kevin Friend, following a viewing by both VAR and the on pitch-side monitor, for elbowing Ashley Westwood.
Buendia had scored Norwich’s only goal of an eight-match losing league run which had confirmed their relegation but with no chance of adding to that tally, the Canaries had to play the best an hour with reduced numbers.
They may have had a lead to protect had Nick Pope – who started his career not far away at Ipswich Town – not made a fine instinctive stop from Godfrey’s header from an early corner, James Tarkowksi blocking the follow-up from Alexander Tettey.
But with a man advantage, the Clarets immediately looked to make them pay as they forced Tim Kruhl into two fine saves before the break.
The Dutchman got down well to keep out a low drive from Jay Rodriguez following Wood’s lay-off and then reacted well to turn a deflected Dwight McNeil free-kick over the bar.
His resistance wouldn’t last much longer, though, once Norwich had been reduced to nine men following Josip Drmic’s dismissal for an over-the-top challenge on Erik Pieters.
That was three minutes into added time at the end of the first half but the Clarets still had time left to grab the lead through that man Wood.
The striker had scored four goals in his previous three top-flight games against Norwich and added another with an acrobatic overhead kick he directed into the bottom corner from Gudmundsson’s cross to become the Clarets’ highest ever scorer for a Premier League season.
Inevitably, Dyche’s men then dominated possession after the break as they went after the second goal that would seemingly put the game to bed.
The Clarets spent long spells camped inside the Norwich half but couldn’t force a way through and with an hour gone Dyche sent on fresh legs in the shape of ex-City wideman Robbie Brady.
Rodriguez saw another effort blocked by Krul from a close-range flick but the Clarets were still grateful for a helping hand to go 2-0 up with 10 minutes to go.
Pieters had been playing virtually as a left winger in the second half and it was his cross that forced the error from Godfrey, whose poor touch guided the ball past Krul into his own net.
Krul did save from substitute Matej Vydra and Phil Bardsley late on to limit the damage for the bottom club, while at the other end Pope had been a virtual spectator.
However, he was alert enough to make a fine save from Onel Hernandez’s deflected effort.
And with a 15th clean sheet in the bag, Pope again goes one clear in the race to win the league’s golden glove at the end of a special season for the Clarets.
Norwich: Krul; Aarons, Godfrey, Klose (Zimmermann HT), Lewis; Tettey (Vrancic 90), McLean; Cantwell (Rupp 76), Buendia, Hernandez (Idah 86); Drmic. Substitutes: McGovern, Stiepermann, Pukki, Famewo, Martin.
Sent off: Buendia, Drmic
Burnley: Pope; Bardsley, Long, Tarkowski, Pieters; Gudmundsson (Brady 60), Westwood, Brownhill, McNeil; Wood (Vydra 79), Rodriguez: Substitutes: Peacock-Farrell, Thompson, Dunne, Benson, Goodridge, Glennon, Mumbongo.
Referee: Kevin Friend